6.1 Ideal Solutions 243
Exercise 6.5
From the following list, pick pairs of substances that you think will probably form nearly ideal
liquid solutions:
o-xylene m-xylene
p-xylene toluene
ethyl benzene 1-propanol
2-propanol naphthalene
anthracene phenanthrene
3-methyl pentane 2-methyl pentane
3-pentanone 2-pentanone
propanal propanoneSolid Solutions
In a solid solution the molecules of two or more substances must fit into a single crystal
lattice. Gold and platinum atoms are nearly the same size and can do this, as can gold
and silver atoms. These elements are completely miscible and form solid solutions that
are nearly ideal. However, most substances cannot fit into the crystal lattices of other
substances and are nearly insoluble in the solid state, even if they form nearly ideal
liquid solutions.Phase Diagrams of Two-Component Ideal Solutions
The phase diagram for a pure substance requires only two axes corresponding toT
andP. In an equilibrium one-phase system with two components, Gibbs’ phase rule
givesfc−p+ 2 2 − 1 + 2 3 (one phase, two components)so that there are three independent intensive variables, which we choose to beTand
Pand one mole fraction. The phase diagram requires three axes. To make a two-
dimensional phase diagram, we must specify a fixed value for one variable.Pressure–Composition Phase Diagrams
In this kind of phase diagram the temperature has a fixed value. The mole fraction of one
component is plotted on the horizontal axis and the pressure is plotted on the vertical
axis. For a two-component ideal solution the partial pressure of both components is
given by Eq. (6.1-2), so that the total vapor pressure isPtotP 1 ∗x 1 +P 2 ∗x 2 P 2 ∗+(
P 1 ∗−P 2 ∗
)
x 1 (two-component ideal solution)
(6.1-23)
where we have used the relationshipx 2 1 −x 1. This equation is represented by a
line segment in the pressure–composition phase diagram.Exercise 6.6
Show that the intercepts of the function in Eq. (6.1-23) atx 1 0 andx 1 1 are equal toP 2 ∗
andP 1 ∗.